Hello, Is there a way to 'invert' an arbitrary Monad? By 'inverting' I mean to turn success into failure and failure into success. Here are some specific inversions of the Maybe and List Monad: invM :: Maybe a -> Maybe () invM Nothing = Just () invM (Just _) = Nothing invL :: [] a -> [] () invL [] = [()] invL (_:_) = [] How can I define this for an arbitrary Monad m? More specifically, I would like to define: inv :: (Monad m, M.MonadPlus m, ???) => m a -> m () inv m = if m fails then return () if m succeeds then fail The following obviously doesn't work: inv m = (m >> mzero) `mplus` return () because it will always return (). There's also a 'inversion' for natural numbers: invN :: Int -> Int invN 0 = 1 invN n = 0 but how can I define that without pattern matching, so only using arithmetic operations, +, -, *, ^, ...? The reason I ask this is that I'm writing a parser combinator library to understand parser a bit better. And I would like to define the combinator: notFollowedBy :: P t m a -> P t m () 'notFollowedBy p' fails when p succeeds and returns () when p fails. I will share the code when it's a bit more polished. Thanks, Bas